Workshop 5

Changing Course Due to Unexpected Conditions

About the Workshop

One minute you're sailing along smoothly, and the
next minute you've run aground. Despite careful planning, lessons do not
always proceed as expected -- an activity prepared by the teacher simply
does not work, or students complete an activity successfully but have difficulty
making sense of what they've done. In this workshop, we'll consider ways
to diagnose conditions mid-lesson, and we'll explore a teacher's options
when things go awry.

The Great Bean Bag Adventure

We now have some sense of what a seed needs to
sprout. However, some of our results left us wondering if a seed will sprout
in liquids other than water. In our third experiment, we explored a number
of unusual liquids to find out how they would affect seed growth.

What we did:
Folded and placed two paper towels in each baggie.Labeled and prepared the baggies as follows:

condition

Seed + water (control)

Seed + vinegar

Seed + diluted dish soap

Seed + salt water

Seed + baby oil

Seed + sugar water

preparation

3 beans; water

3 beans; vinegar*

3 beans; diluted dish soap*

3 beans; salt water*

3 beans; baby oil*

3 beans; sugar water*

*The liquids were added directly on top of and
around the beans. Enough was added to thoroughly coat the surface of the
paper towel around the beans, but not so much that the beans were sitting
in a pool of liquid.

Getting Ready (15 min. each)

For this workshop, you were asked to prepare
two short narratives. In groups of three, take turns sharing the narrative
that you wrote from your own perspective as a teacher. After each narrative
is read, discuss possible next moves for the situation described.

In same small group, take turns sharing the narrative
that you wrote from the perspective of your student. As each narrative
is read, listen carefully for recurring themes -- experiences that you
imagine to be common to many students when they are having difficulty making
meaning of an activity. After each narrative is read, discuss possible
next moves that seem appropriate given the needs and perspectives of the
student. How do these next moves compare to those discussed earlier?

Site Conversation 1 (5 min.)

The questions that a teacher asks often have a profound effect on students'
ability to move from their own ideas to the teacher's intended learning
goal. What are the characteristics of a "good" question, one that
successfully guides student thinking in the right direction?

Site Conversation 2 (5 min.)

Tricia says that teaching is like a dance -- a slow dance -- and teachers
need to let students lead. Does this dance analogy work in your classroom?
Do you always let students lead? When (if ever) is it important for the
teacher to lead?

Going Further

What are some of the circumstances that can cause a lesson or an activity
to fall apart? Generate a group list. Categorize your list and look for
patterns.

Discuss ways that teachers can "take the temperature" midway
through a lesson or activity in order to prevent things from going off
course.

Homework for Workshop 6

Choose one of the five Try This! activities that you have seen
thus far (Pattern Puzzles, Classroom Landfill, 'Round About pi, Swingers,
and Sorting Socks). On a level that is appropriate for your students,
make a list of the content goals for learning for this activity, and bring
your list of content goals with you to Workshop 6.

TRY THIS!

Sorting Socks

Suggested Grade Level: K-2

Students build a floor graph of common objects that they collect, and
then turn the information into a bar graph.

What you need

Graph paper
Butcher paper

Prepare a piece of butcher paper to be the base
for the floor graph. Along the bottom of the paper, draw a line. Draw tick-marks
along the line. These will help to orient the different categories to be
graphed.

What to do

Several days before you plan to do this activity, ask every student
to bring in one sock (you could also do this activity using mittens, empty
soda cans, empty cereal boxes, etc.).

On the day of the activity spread out the socks for all students to
see.

Spend time with students describing the differences and similarities
of the socks. For example, students might describe and organize the socks
by color, by size, or by material.

Students can take turns putting the socks in piles of the same type.
For example, if students organize the socks by color, they might make a
pile for blue socks, a pile for red socks, a pile for white socks and a
pile for patterned socks.

Floor Graph

Roll out the prepared butcher paper on the floor.

Below each tick-mark, write the name of a pile-type.

Have students line the different types of socks above the appropriate
tick-marks making a "graph" representing the different types
of socks.

Help students understand their categorizing by asking the following questions:

Count each type of sock to determine which has the most. Which has
the least?

Do any of the lines have the same amount?

Bar graphs

Along the bottom row of a piece of graph paper, have students write
the name of each pile-type in a separate column.

For each sock on the floor graph, have students fill in one square
above the appropriate label.

After students have completed their bar graphs, remove the socks from
the floor graph and help students understand their bar graphs by asking
the following types of questions:

Which column is the tallest? What does the tallest column represent?

Which column is the shortest? What does the shortest column represent?

Are there any columns that are the same/similar height? What does it
mean when two columns are a similar height?

For older students

Older students can survey their classmates to find out information such
as: "What are your favorite socks?" "Do you wear socks in
the summer?" "What color socks are you wearing today?"

Students can then represent the information they collect on a bar graph.

One connection to the Standards

Standard 2: Mathematics as Communication

In grades K-4, the study of mathematics should include numerous opportunities
for communication so that students can --

reflect on and clarify their thinking about mathematical ideas and
situations;

relate their everyday language to mathematical language and symbols;

realize that representing, discussing, reading, writing, and listening
to mathematics are a vital part of learning and using mathematics.

"Representing is an important way of communicating mathematical
ideas at all levels, but especially so in K-4. Representing involves translating
a problem or an idea into a new form … The act of representing encourages
children to focus on the essential characteristics of a situation. Representing
includes the translation of a diagram or physical model into symbols or
words."

National Council of Teachers of Mathematics, (NCTM). 1989.
Curriculum and evaluation standards for school mathematics. Reston,
VA: The National Council of Teachers of Mathematics. (pg. 26)